The Grande Armee of 1805 was arguably the best Napoleon ever led. They had gone through almost three years of intensive training in the Channel camps with the emphasis being of infantry/artillery cooperation on the battlefield. None of the armies they faced in 1805 had this great advantage.
Further, the French military reform period from 1763-1789 had initiated and/or developed staff organization and functioning, the development of the division as a tactical organization, the excellent artillery reforms that remade the French artillery arm and finally developed field artillery as distinct to siege artillery.
The field maneuvers in Normandy in the 1770s developed the tactics that would be employed beginning in the 1790s during the French Revolutionary Wars. Some of the results of the experimentation were the excellent expeditionary force under Rochambeau that was sent to assist the Americans in 1780, including the new artillery pieces of the Gribeauval System.
The corps system was first employed in the Marengo campaign of 1800 and was then fully integrated into the Grande Armee. The French staff system was superior to anything the allies employed as well as the system of divisions that made up the individual corps.
The French corps d'armee was essentially a corps headquarters for command and control with corps troops assigned to it (engineers, gendarmes, and support troops). This could control from two to five infantry divisions and would also have either a brigade or division of light cavalry assigned to it.
If the situation demanded or an opportunity presented itself divisions of either infantry or cavalry could be attached or detached between corps and other corps could be temporarily organized as in 1805, 1807, and 1809 with little or no loss of efficiency.
The flexibility of the corps d'armee system enabled command and control to be decentralized and the corps themselves were organized both to the merits and capabilities of the individual corps commanders and to confuse enemy intelligence.
Horse artillery made its debut in the French service in 1792 and Napoleon introduced a militarized artillery train in 1800.
Napoleon also organized the Cavalry Reserve which was a corps organization of cavalry and supporting artillery and other corps units commanded by the army cavalry commander.
Each corps had both an engineer and artillery commander, the latter usually being an artillery general officer.
There was also an army artillery reserve under the command of the army artillery chief, a senior artillery officer.
No other army of the period was organized from 1805 in such a manner, though some armies adopted the corps system later in the wars.
Neither the Austrians nor the Russians were trained to this standard and their organizations above the regiment were not permanent organizations and the units were formed into ad hoc higher-level organizations at the beginning of a campaign from units that had not trained together to the same standard.